A thermostat showing nothing at all is almost always dead batteries or a lost 24-volt supply rather than a broken furnace. If the screen is live but the heat never comes on, check the mode and the schedule first, since a unit left on cool or on an unexpected programme will not call for heat. Beyond that the causes are a tripped furnace door switch, a blown low-voltage fuse on the control board, or corroded wiring at the thermostat base.
Smart thermostat installs on older Ohio furnaces frequently fail for one specific reason: no common wire. Many pre-1990 systems were wired without one, and the workarounds vary by equipment. An HVAC professional can confirm the wiring before you buy hardware that will not work. Pro HVAC connects homeowners in Upper Arlington, OH with professionals who handle this. Call (321) 463-9811.